Question

24 multiple choice 4 points
an urn contains five red marbles, four green marbles, and three blue marbles. if one
marble is drawn at random, what is the probability that it is either a green marble or
a blue marble?
$\frac { 7 } { 12 }$
$\frac { 3 } { 12 }$
$\frac { 5 } { 12 }$
$\frac { 4 } { 12 }$
25 multiple choice 4 points
a single card is drawn from a standard deck of 52 cards. what is the probability the
card is a five or a diamond?
$\frac { 18 } { 52 }$
$\frac { 15 } { 32 }$
$\frac { 17 } { 52 }$
$\frac { 16 } { 52 }$

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(5 + 4+3=12\)

Step2: Calculate number of favorable marbles

Favorable marbles (green + blue) = \(4 + 3=7\)

Step3: Calculate probability

Probability \(P=\frac{\text{Favorable}}{\text{Total}}=\frac{7}{12}\)

for card problem:

Step1: Calculate number of fives

There are 4 fives in a deck.

Step2: Calculate number of diamonds

There are 13 diamonds in a deck.

Step3: Subtract the overlap (the five of diamonds)

Overlap is 1 card.
Favorable cards \(=4 + 13-1=16\)

Step4: Calculate probability

Probability \(P=\frac{16}{52}\) (Option D)

Answer:

\(\frac{7}{12}\) (Option A)